The present invention relates generally to the recovery of independent user signals simultaneously transmitted through a linear mixing channel, and more particularly, to a method and system for blind recovery of a number of independent user signals.
In many signal processing applications, the sample signals provided by the sensors are mixtures of many unknown sources. The xe2x80x9cseparation of sourcesxe2x80x9d problem is to extract the original unknown signals from these known mixtures. Generally, the signal sources as well as their mixture characteristics are unknown. Without knowledge of the signal sources other than the general statistical assumption of source independence, this signal processing problem is known in the art as the xe2x80x9cblind source separation problemxe2x80x9d. The separation is xe2x80x9cblindxe2x80x9d because nothing is known about the values of the independent source signals and nothing is known about the mixing process (which is assumed to be linear).
The blind separation problem is encountered in many familiar forms. For instance, the well-known xe2x80x9ccocktail partyxe2x80x9d problem refers to a situation where the unknown (source) signals are sounds generated in a room and the known (sensor) signals are the outputs of several microphones. Each of the source signals is delayed and attenuated in some (time varying) manner during transmission from source to microphone, where it is then mixed with other independently delayed and attenuated source signals, including multipath versions of itself (reverberation), which are delayed versions arriving from different directions. A person, however, generally wishes to listen to a particular set of sound source while filtering out other interfering sources, including multi-path signals.
This signal processing problem arises in many contexts other than the simple situation where each of two mixtures of two speaking voices reaches one of two microphones. Other examples involving many sources and many receivers include the separation of radio or radar signals sensed by an array of antennas, sonar array signal processing, image deconvolution, radio astronomy, and signal decoding in cellular telecommunication systems. Those skilled in the signal processing arts have been eager to solve blind source separation problems because of their broad application to many communication fields. Solutions to date, however, are time intensive, require extensive computing power, and the source signal separation is not ideal.
The present invention broadly contemplates systems and methods for blind source separation based on the identification of a set of conditions which are necessary and sufficient for the separation of the source signals and which any method used for blind source separation must satisfy. Preferably, an optimization technique is used to enforce these conditions to separate and recover the source signals. This approach achieves better signal separation than known processes, and the optimization reduces the time and computing needed to separate the source signals.
In accordance with the present invention, a simple constrained criterion which stems directly from derived conditions for source separation is identified. Using this criterion, observed, i.e., first signals, and output signals are used to control a filtering matrix. After being initialized, the filtering matrix is updated and projected to the closest unitary matrix. Until the filtering matrix has converged, it continues to be updated and projected to the closest unitary matrix. Once convergence has occurred, the source signals have been recovered.